Conventionally, there is an air conditioning system in which a mobile terminal held by a user outside his house remotely controls an air conditioner in the house. For example, Patent Literature 1 described below discloses a technique in which a mobile terminal estimates the time at which a user comes home based on the position and the moving speed of the mobile terminal and position information of his house, to control the air conditioner according to a registered control pattern, so as to be able to provide a comfortable environment for the user at the arrival time.